The Default model in [1]}, [2]} models the distribution of the magnitude of the BH spin vector and the tilt angle between the spin vector and the orbital angular momentum. They adopt a Beta distribution for the spin magnitude model [3]}, [1]},
\(\pi (a_{1,2}| \alpha _\chi , \beta _\chi ) = \textrm {Beta}(a_{1,2}|\alpha _\chi , \beta _\chi ),\) 
